Controlled-source Electromagnetic Modeling And Inversion Using Finite Element Method For The Complex Media

The Controlled-source electromagnetic method(CSEM)is a commonly used technique in geophysical exploration.Due to its low cost,large exploration depth and strong anti-interference ability,it has been widely used in mineral exploration,geological mapping,and environmental and engineering investigations.Recently,with the development of CSEM instruments and the improvement of data acquisition technology,both academia and industry collected large amounts of three-dimensional(3D)CSEM data.However,compared to the abundance of data,the ability to process and interpret data is a major bottleneck that limits our insight into the Earth's internal information.At present,the numerical simulation algorithms of CSEM data are mostly based on the isotropic conductivity of the earth medium,ignoring the effects of conductivity anisotropy,dispersion and magnetization effects,which may lead to the misunderstanding of underground structures and these algorithms can only be applied to specific CSEM systems.Moreover,the 3D inversion techniques are not yet mature,and there are many problems such as low computational efficiency,poor compatibility,and inability to deal with complex geological models.To solve these problems,a novel 3D CSEM numerical simulation algorithm which allow for conductivity anisotropy,dispersion and magnetically permeable heterogeneities is developed.We analyzed influences of different electromagnetic properties on the CSEM responses in frequency and time domain.At the same time,we realized the 2.5-dimensional anisotropic inversion and 3D inversion algorithms in frequency domain and discussed the inversion results under the conditions of conductivity anisotropy and topographyIn forward modeling,we present a 3D CSEM numerical simulation algorithm in the complex media based on a secondary field formulation and finite element method.To overcome the problem of spurious solutions used by conventional nodal basis functions,we use an edge-based finite element which can satisfy the tangential continuity of the electromagnetic field and eliminate no-physical solutions.After finite analysis,the large sparse system is solved by a parallel direct solver.Therefore,the time domain response can be efficiently calculated by a cosine transform from frequency domain.This newly developed scheme allows us to analyse the influences of conductivity anisotropy,dispersion,and magnetization on frequency-domain and time-domain CSEM data.Several numerical examples validate the accuracy and efficiency of our algorithm and demonstrated it can be appled to model land,airborne,and marine CSEM applications.The magnetic permeability and chargeability of the earth's media have an important impact on the CSEM data.However,most of the 3D forward modeling algorithms do not consider these complex factors,which will introduce errors to the interpretation results.In this paper,the anomalous magnetic permeability is added to the 3D forward calculation,and the dispersion characteristics of the earth's conductivity are described by a Cole-Cole relaxtion model.We use several numerical examples to analyse the influence of anomalous magnetic permeability and dispersion effect on the CSEM responses,and we proposed a method for identifying the characteristics of chargeability in earth medium.In the inversion part,although 3D inversion can obtain more accurate electrical distribution,considering the actual computing efficiency and memory constraints,2D inversion with topography still has tremendous advantages in real data inversion.We realized the marine CSEM 2.5-D anisotropy inversion based on Tikhonov regularization.In order to simulate the seabed topography and irregular anomalous bodies,the computational domain is divided into unstructured grids.Considering the multi frequency and multi field sources of marine CSEM,we adopts MPI parallel technology to accelerate and improve the efficiency of the inversion.The synthetic data and real data validate the accuracy and efficiency of our algorithm.Finally,a data-space variant of the nonlinear conjugate gradient(DCG)algorithm has been developed for the 3D CSEM inversion problem.Model-space approach makes it difficult to run 3D CSEM inversion on a personal computer because of large computational costs;however,a data-space approach which the size of matrix depend on the data rather than the model parameters can solve this difficulty very well.To reduce memory requirements,a CG optimization technique is used for minimizing the objective function.Synthetic tests show that 3D CSEM inversion based on data-space method can significantly reduce their storage and computational requirements.